Countable multiplicity and category

Authors

  • Yu.Yu. Trokhimchuk

DOI:

https://doi.org/10.15407/dopovidi2014.01.033

Keywords:

category, countable multiplicity, homeomorphism

Abstract

For a continuous mapping of finite-dimensional manifolds, it is proved that it has points of a local homeomorphism if, for some set of its image-points not of the first category, its multiplicity is at most countable.

Downloads

Download data is not yet available.

References

Aleksandrov P. S. Dokl. AN USSR, 1936, No. 4: 283–288 (in Russian).

Trokhymchuk Yu. Yu., Safonov V. M. Zb. prats Inst. matematyky NAN Ukr., 2013, 10, No. 4–5: 526–531 (in Russian).

Trokhymchuk Yu. Yu., Differentiation, inner mappings, and analyticity criteria. Kyiv: Institute of Mathematics NAS of Ukraine, 2007 (in Russian).

Luzin N. N. Lectures on analytic sets and their applications. Moscow, 1970 (in Russian).

Kuratovsky K. Topology. Vol. 1. Moscow: Mir, 1966 (in Russian).

Downloads

Published

24.03.2025

How to Cite

Trokhimchuk, Y. (2025). Countable multiplicity and category . Reports of the National Academy of Sciences of Ukraine, (1), 33–36. https://doi.org/10.15407/dopovidi2014.01.033

Issue

No. 1 (2014): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

License

Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.